Monday, April 11, 2016

General Relativity and the dimension of reality

When people first hear of General Relativity and the idea that spacetime is curved, they naturally imagine a higher-dimensional uncurved space in which our four-dimensional spacetime curvily sits. They may even be shown pictures of a two-dimensional sheet warping into three dimensions. But it's usually then explained to them that that's a misleading way to look at things: reality is just four-dimensional, but has a metric that makes it behave like it's curving in a higher-dimensional space.

What if the natural way of thinking about this is right? What if, say, reality is an 89-dimensional Euclidean space with signature (2,87), but physical objects are constrained to live on a 4-dimensional subset of it? The constraint could be effected, for instance, by a global discontinuous scalar field on the 89-dimensional space that takes two values: 1=allowed and 0=forbidden.

I suppose the main reason not to go for an ontology like this for General Relativity is that it's messier.

1 comment:

It seems Occam's Razor would cut against postulating each extra dimension without getting some explanatory payoff. Postulating the constraining field makes sense explanatorily, though somehow people think it's a violation of Occam's Razor when the Neo-Lorentzian's do something similar to explain relativistic effects rather than embracing the deeply counter-intuitive and absurd consequences of Minkowskian STR... even though Bell's thread does in fact break!.... But I digress.

If nothing else, though, this sort of speculation furnishes a good case-in-point for an argument like you and Leftow give for the existence of God: from unrealized possibilities of this grand sort.

About Me

I am a philosopher at Baylor University. This blog, however, does not purport to express in any way the opinions of Baylor University. Amateur science and technology work should not be taken to be approved by Baylor University. Use all information at your own risk.